Anna KarlinMost Slides by Alex Tsun

Poisson RV Example

The Zoo of Discrete RV’s

probability students

Definition ofExpectation

● The Bernoulli RV● The Binomial RV● The Geometric RV● The Uniform RV● The Poisson RV

● The Negative Binomial RV● The Hypergeometric RV

random variables

Important Examples:

Uniform(a,b):

Bernoulli(p): P(X = 1) = p, P(X = 0) = 1-p μ = p, σ2= p(1-p)

Binomial(n,p) μ = np, σ2 = np(1-p)

Poisson(λ): μ = λ, σ2 = λ

Bin(n,p) ≈ Poi(λ) where λ = np fixed, n →∞ (and so p=λ/n → 0)

Geometric(p) P(X = k) = (1-p)k-1p μ = 1/p, σ2 = (1-p)/p2

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Probability4.1 Continuous random Variables

BasicsAnna Karlin

Most Slides by Alex Tsun

Agenda● Probability Density Functions (PDFs)● Cumulative Distribution Functions (CDFs)● From Discrete to Continuous

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probability students

Definition ofExpectation

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Probability4.2 Zoo of Continuous RVs

Agenda● The (Continuous) Uniform RV● The Exponential RV● Memorylessness

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